The man has been identified as 42-year-old Semion Mosheshvili of Hewlett, Long Island, who turned himself in early Sunday morning.
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He is charged with criminal possession of a weapon, reckless endangerment, and acting in a way injurious to a child under 17 years of age.
Police say the licensed owner of the gun is the female owner of the home on Deisius Street in Prince's Bay.
The incident happened during a family gathering at about 7 p.m. Saturday.
The woman apparently gave the gun to Mosheshvili and it went off, authorities say.
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The bullet went through the floor, striking the 10-year-old on a lower floor who was hit in the shoulder.
His mother drove him to the hospital and he did not need surgery. The boy is in stable condition.
Mosheshvili initially fled the scene but turned himself in shortly after midnight.